We investigate low-lying bound states of the neutron-rich nucleus 15 B by assuming it is a three-body system made of an inert core 13 B and two valence neutrons. The three-body wave functions are obtained using the Faddeev formalism. Special attention is paid to the excited state at 3.48(6) MeV observed in the 13 C( 14 C, 12 N) 15 B reaction, whose properties are less clear theoretically. In our three-body model, besides the ground state 3/2 − 1 , a second 3/2 − 2 state is discovered at around 3.61 MeV, which might be identified with the excited state observed at 3.48(6) MeV. We study this 3/2 − 2 state in detail, which turns out to be a two-neutron halo state with a large matter radius rm ≈ 4.770 fm.